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Ch 3 Practice

# E a unit of good 1 is combined with a unit of good 2

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Unformatted text preview: (go over the intuition once and for all): Contrast The following graphs are for the problem: In each case, look at change in with Lagrangian method due to an infinitesimally small increase in 8 ECO 204 Chapter 3: Practice Problems & Solutions for Utility Maximization in ECO 204 (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. {( (3.3) Show if the following utility functions, defined over (a) ( ) and ) }, have identical indifference curves: ? Show all calculations. Answer ( ). As such, the both True. The utility function is a positive monotonic transformation of represent the same preferences and graphically will have the same indifference curves (albeit with differing numbers) | (why not check if this is true?). Here is the positive monotonic transformation: and identical | ( ) Notice that when we do positive monotonic transformations we leave alone the term microeconomics). (b) ( ) and ? Show all calculations. False. The utility function is not a positive monotonic transformation of ( This is not the same as (it be the Chuck Norris of ( ): ) . (3.4) Graph an indifference curve for an arbitrary level of utility ● give expressions for the indifference curve equation, intercepts and slope ● and state (but do not solve) as simplified as possible UMP. Show all calculations. ( C) . [Hint: Do a positive monotonic transformation] Answer: Do a positive monotonic transformation so we can work with an easier utility function: 9 ECO 204 Chapter 3: Practice Problems & Solutions for Utility Maximization in ECO 204 (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. The equation of an indifference curve corresponding to an arbitrary level of utility For the y-axis intercept set However, is: : undefined which means there is no y-axis intercept. For the x-axis intercept set : The slope of the indifference at any bundle in the consumption set is: When slope is Notice that (y-axis “intercept” – using this word carelessly) the slope is and when (x-axis intercept) the Thus, the indifference curve looks like: whenever and Hence the UMP can be written as: 10 ECO 204 Chapter 3: Practice Problems & Solutions for Utility Maximization in ECO 204 (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. (d) . Answer: The equation of an indifference curve corresponding to an arbitrary level of utility ( For the y-axis intercept set ) : For the x-axis intercept set is: : The slope of the indifference at any bundle in the consumption set is: When (y-axis “intercept”) the slope is and when (x-axis intercept) the slope is Thus, the indifference curve looks like: 11 ECO 204 Chapter 3: Practice Problems & Solutions for Utility Maximization in ECO 204 (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Notice that whenever and Hence the UMP can be written as: (3.5) A consumer has the following utility function defined over Suppose and that {( ) }: and Without solving the UMP, what is impact on the consumer’s utility due to...
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